1. Field of the Invention
This invention relates generally to the analysis of wells penetrating subterranean formations, and more particularly, the determination of subsurface formation properties such as pressure, permeability and the like in perforated wells.
2. Description of Related Art
Various fluids such as oil, water and natural gas are obtained from a subterranean geologic formation, referred to as a reservoir, by drilling a well that penetrates the fluid-bearing formation. Once a wellbore has been drilled, the well must be completed before fluids can be produced from the well. Well completion involves the design, selection, and installation of equipment and materials in or around the wellbore for conveying, pumping, and/or controlling the production or injection of fluids. After the well has been completed, production of fluids can begin.
Typically, wells are either cased or open hole wells. An open hole well is usually just a wellbore that is drilled into the ground or ocean floor. A cased well is an open hole well with a tubular steel casing inserted therein to line the sidewall of the wellbore. Cement is pumped downhole into the wellbore and forced uphole into an annulus between the casing and the sidewall of the wellbore to secure the casing in place.
It is often necessary to perforate the sidewall of the wellbore of cased or open hole wells to allow fluid to flow from the formation into the wellbore as shown in FIG. 1. Penetration may be achieved in open hole wells by punching or drilling a hole or perforation into the sidewall of the wellbore. However, in cased holes, it is necessary to puncture or drill through the casing and cement before the sidewall of the wellbore may be penetrated and the formation reached. Various techniques for penetrating the sidewall of the wellbore of cased and/or open hole wells have been heretofore developed. An example of such a technique for creating a perforation which involves extending a drill bit through the casing and into the formation using a downhole tool with a flexible drill shaft may be seen in U.S. Pat. No. 5,692,565, the entire contents of which is hereby incorporated by reference.
It is often desirable to determine various characteristics of the well and its penetrated formation. By analyzing the characteristics of the well and the formation, it is possible to obtain information that may help to determine how the well will produce. Various techniques have been developed to determine characteristics of the wellbore. For example, so called xe2x80x9cformation testing toolsxe2x80x9d have been developed to provide logging in cased wellbores as exemplified by U.S. Pat. Nos. 5,065,619; 5,195,588; and 5,692,565, the entire contents of which are hereby incorporated by reference.
The ""619 patent discloses a means that penetrates the formation for testing the pressure of a formation behind casing in a wellbore. A xe2x80x9cbackup shoexe2x80x9d is hydraulically extended from one side of a wireline formation tester for contacting the casing wall, and a testing probe is hydraulically extended from the other side of the tester. The probe includes a surrounding seal ring that forms a seal against the casing wall opposite the backup shoe. A small explosive shaped charge is positioned in the center of the seal ring for perforating the casing and surrounding cement layer, if present. Formation fluid flows through the perforation and seal ring into a flow line for delivery to a pressure sensor and a pair of fluid manipulating and sampling tanks.
The ""588 patent improves upon the formation testers that perforate the casing to obtain access to the formation behind the casing by providing a means for plugging the casing perforation. More specifically, the ""588 patent discloses a tool that is capable of plugging a perforation while the tool is still set at the position at which the perforation was made. Timely closing of the perforations(s) by plugging prevents the possibility of substantial loss of wellbore fluid into the formation and/or degradation of the formation. It also prevents the uncontrolled entry of formation fluids into the wellbore, which can be deleterious such as in the case of gas intrusion.
The ""565 patent describes a further improved apparatus and method for testing a formation behind a cased wellbore, in that the invention uses a flexible drilling shaft to create a more uniform casing perforation than with a shaped charge. The uniform perforation provides greater reliability that the casing will be properly plugged, because the explosive shaped charges result in non-uniform perforations that can be difficult to plug. Thus, the uniform perforation provided by the flexible drilling shaft increases the reliability of using plugs to seal the casing. The drilling shaft can also be used to test the formation at differing distances from the wellbore. By testing the pressure transient characteristics of the perforation at varying distances from the wellbore, a more precise model of the near wellbore formation damage can be obtained.
While various tools have been developed to test formations, there remains a need for estimating the reservoir characteristics based on the known parameters and/or measured data. Models and other conventional formation tester analysis techniques have been developed to estimate the properties of the formation. One such mathematical model, depicted in FIG. 2, has been used to determine various formations parameters as set forth in the publication entitled xe2x80x9cAnalytical Models for Multiple Formation Testerxe2x80x9d by P. A. Goode and R. K. M. Thambynayagam, SPE Formation Evaluation, December 1992, p. 297-303 (xe2x80x9cSPE 20737xe2x80x9d) the entirety of which is hereby incorporated by reference. The analytical model of SPE 20737 uses the pressure transient response to determine the pressure and permeability of the subterranean formation.
Data collected by the tool, as fluid flows from the formation, may be used to determine formation characteristics based on a mathematical model. The mathematical model set forth in the SPE paper 20737 may be used to determine various formation properties from the pressure and fluid data collected. According to SPE 20737, formation properties, such as pressure and permeability may be estimated using the mathematical model. The model of FIG. 2 assumes that the formation fluid is permitted to exit the formation through the hole and enter a wellbore or a tool. Fluid flow patterns are generally spherical as they approach a hole, and became generally radial further away from the hole. Notably absent from the mathematical model depicted in FIG. 2 is the perforation extending into the formation.
Another mathematical model used to determine various formations parameters is xe2x80x9cA Perturbation Theorem for Mixed Boundary Value Problems in Pressure Transient Testingxe2x80x9d by D. Wilkinson and P. Hammond (Transport in Porous Media (1990) 5, 609-636), the entire contents of which is hereby incorporated by reference. The analytical model of the paper by Wilkinson and Hammond uses the pressure transient response during the drawdown period of a pressure test to determine the mobility of the formation and fluid. However, both of the models fail to take into consideration the effect of perforations extending into the wellbore when determining formation parameters.
The present invention overcomes the inadequacies of the previous methods by providing a method for determining various formation parameters while taking into consideration the alteration in the fluid characteristics resulting from the perforation.
The present invention relates to a method for determining the characteristics of a formation penetrated by a wellbore. The method involves creating a perforation having a hole radius and a length in the formation. An equivalent probe radius value is calculated for the perforation based upon the hole radius and length. Formation analysis calculations may then be performed using the equivalent probe radius in lieu of the hole radius.
The present invention also relates to a method for calculating formation properties in a subterranean formation penetrated by a wellbore, the wellbore having a perforation extending into the subterranean formation. The method relates to determining a radial hole radius and length of the perforation, calculating an equivalent probe radius for the perforation, and using the equivalent probe radius as the radial hole radius in formation analysis calculations.
A method of formation analysis for a formation penetrated by a wellbore is also disclosed. The method involves creating a cylindrical hole extending from the wellbore, the cylindrical hole having a known radius and first length, calculating an equivalent probe radius based upon the hole radius and first length, conducting formation analysis tests, and adjusting the model utilizing the equivalent probe radius in place of the hole radius, thereby calculating initial wellbore formation properties. The cylindrical hole is then extended further into the formation, thereby creating a second length. The equivalent probe radius may then be determined for the second length thereby calculating extended wellbore formation properties.
Another aspect of the invention relates to a method of generating a reservoir property profile around a wellbore. The method relates to sequentially extending a perforation to differing distances from the wellbore into the formation, calculating an equivalent probe radius (rpe) for each different perforation length based upon the perforation radius (rp) and the formation length (Lpf) in the formation using the following formula:
rpe=SQRT[rp*(rp+2*Lpf)],
conducting reservoir analysis tests at each different perforation length, performing reservoir analysis calculations using the equivalent probe radius in place of the perforation radius to determine reservoir properties at each of the different perforation lengths, comparing the reservoir properties for each of the perforation lengths, and generating a reservoir property profile at various distances from the wellbore.
The present invention also relates to a method of adapting conventional formation analysis techniques. The method relates to providing a perforation into the formation, the perforation having a radius and a length, calculating an equivalent probe radius for the perforation, based upon the perforation radius and formation length and an equivalent probe radius formula, and performing conventional formation analysis calculations utilizing the equivalent probe radius in lieu of the perforation radius value.